Physics
Total Mechanical Energy
Total mechanical energy is the sum of an object's kinetic energy and potential energy. It represents the overall energy of a system due to its motion and position. In the absence of non-conservative forces like friction, the total mechanical energy of a system remains constant, following the principle of conservation of energy.
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7 Key excerpts on "Total Mechanical Energy"
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
(8-1) If the particle moves from point x i to point x f , the change in the potential energy of the system is ΔU = − ∫ x f x i F(x)dx. (8-6) Gravitational Potential Energy The potential energy asso- ciated with a system consisting of Earth and a nearby particle is gravitational potential energy. If the particle moves from height y i to height y f , the change in the gravitational potential energy of the particle–Earth system is ∆U = mg( y f − y i ) = mg ∆y. (8-7) If the reference point of the particle is set as y i = 0 and the cor- responding gravitational potential energy of the system is set as U i = 0, then the gravitational potential energy U when the Review & Summary particle is at any height y is U( y) = mgy. (8-9) Elastic Potential Energy Elastic potential energy is the energy associated with the state of compression or extension of an elastic object. For a spring that exerts a spring force F = −kx when its free end has displacement x, the elastic potential energy is U(x) = 1 2 kx 2 . (8-11) The reference configuration has the spring at its relaxed length, at which x = 0 and U = 0. Mechanical Energy The mechanical energy E mec of a system is the sum of its kinetic energy K and potential energy U: E mec = K + U. (8-12) An isolated system is one in which no external force causes energy changes. If only conservative forces do work within an isolated sys- tem, then the mechanical energy E mec of the system cannot change. This principle of conservation of mechanical energy is written as K 2 + U 2 = K 1 + U 1 , (8-17) in which the subscripts refer to different instants during an energy transfer process. This conservation principle can also be written as ∆E mec = ∆K + ∆U = 0.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ The kinetic energy portion of the internal energy gives rise to the temperature of the system. Statistical mechanics relates the pseudo-random kinetic energy of individual particles to the mean kinetic energy of the entire ensemble of particles comprising a system. Furthermore it relates the mean kinetic energy to the macroscopically observed empirical property that is expressed as temperature of the system. This energy is often referred to as the thermal energy of a system, relating this energy, like the temperature, to the human experience of hot and cold. Internal energy changes Interactions of thermodynamic systems Type of system Mass flow Work Heat Open Closed Isolated Thermodynamics is chiefly concerned only with the changes, Δ U , in internal energy: The most important parameters in thermodynamics when considering the changes in total energy are the changes due to the flow of heat Q and due to mechanical work, i.e. changes in volume and pressure of the system. Accordingly, the internal energy change Δ U for a process may be written more specifically as where Q is heat added to a system and W mech is the mechanical work performed due to pressure or volume changes in the system. All other perturbations and energies added by other processes, such as an electric current introduced into an electronic circuit, is summarized as the term W extra . When a system is heated, it receives energy in form of heat. This energy increases the internal energy. However, it may be extremely difficult to determine how this extra energy is stored. In general, except in an ideal gas, it is redistributed between kinetic and potential energy. The net increase in kinetic energy is measurable by an increase in the temperature of the system. The equipartition theorem states that increase in thermal energy is distributed between the available degrees of freedom of the fundamental oscillators in the system.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
Internal Energy In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy necessary to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal energy has two major components, kinetic energy and potential energy. The kinetic energy is due to the motion of the system's particles (translations, rotations, vibrations), and the potential energy is associated with the static constituents of matter, static electric energy of atoms within molecules or crystals, the static energy of chemical bonds. The internal energy of a system can be changed by heating the system or by doing work on it; the first law of thermodynamics states that the increase in internal energy is equal to the total heat added and work done. If the system is isolated, its internal energy cannot change. For practical considerations in thermodynamics or engineering it is rarely necessary, nor convenient, to consider all energies belonging to the total intrinsic energy of a sample system, such as the energy given by the equivalence of mass. Typically, descriptions only include components relevant to the system under study. Thermodynamics is chiefly concerned only with changes of the internal energy. The internal energy is a state function of a system, because its value depends only on the current state of the system and not on the path taken or process undergone to arrive at this state. It is an extensive quantity. The SI unit of energy is the joule. Sometimes physicists define a corresponding intensive thermodynamic property called specific internal energy , which is internal energy per a unit of mass of the system in question. As such, the SI unit of specific internal energy is J/kg. If intensive internal energy is expressed per amount of substance, then it is referred to as molar internal energy and the unit is J/mol.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
If work W is done on the system, then W = ∆E = ∆E mec + ∆E th + ∆E int . (8.5.1) If the system is isolated (W = 0), this gives ∆E mec + ∆E th + ∆E int = 0 (8.5.2) and E mec,2 = E mec,1 − ∆E th − ∆E int , (8.5.3) where the subscripts 1 and 2 refer to two different instants. Power The power due to a force is the rate at which that force transfers energy. If an amount of energy ∆E is transferred by a force in an amount of time ∆t, the average power of the force is P avg = ∆E _ ∆t . (8.5.6) The instantaneous power due to a force is P = dE _ dt . (8.5.7) The reference configuration has the spring at its relaxed length, at which x = 0 and U = 0. Mechanical Energy The mechanical energy E mec of a sys- tem is the sum of its kinetic energy K and potential energy U: E mec = K + U. (8.2.1) An isolated system is one in which no external force causes energy changes. If only conservative forces do work within an isolated system, then the mechanical energy E mec of the system cannot change. This principle of conservation of mechanical energy is written as K 2 + U 2 = K 1 + U 1 , (8.2.6) in which the subscripts refer to different instants during an energy transfer process. This conservation principle can also be written as ∆E mec = ∆K + ∆U = 0. (8.2.7) Potential Energy Curves If we know the potential energy function U(x) for a system in which a one-dimensional force F(x) acts on a particle, we can find the force as F(x) = − dU(x) _ dx . (8.3.2) If U(x) is given on a graph, then at any value of x, the force F(x) is the negative of the slope of the curve there and the kinetic energy of the particle is given by K(x) = E mec − U(x), (8.3.4) where E mec is the mechanical energy of the system. A turning point is a point x at which the particle reverses its motion (there, K = 0). The particle is in equilibrium at points where the slope of the U(x) curve is zero (there, F(x) = 0).
eBook - PDFThe Silicon Web
Physics for the Internet Age
- Michael G. Raymer(Author)
- 2009(Publication Date)
- CRC Press(Publisher)
These limits are discussed in Chapter 4. To summarize the two general types of energy: Mechanical potential energy is the energy that is stored in objects by virtue of their positions. This stored energy can potentially be released later and cause some work to be done. Examples of potential energy include gravita-tional potential energy gained when you climb (or someone pushes you up) a ramp, chemical energy stored in your muscles, and electrical energy stored in a battery. Kinetic energy is the energy associated with a moving object. An example of kinetic energy is a moving skateboard and rider. 3.6 THE CONSTANCY OF ENERGY This leads us to the most important principle about energy—its constancy or conservation. ◾ ◾ ◾ ◾ ◾ FIGURE 3.21 The behavior of atoms in a gas, liquid, or crystalline solid (a crystal). Gas Liquid Crystalline solid QUICK QUESTION 3.4 Think of other examples in which thermal energy can be used to do work. Mechanics 73 Mechanics Principle (iv) Energy conservation principle: Energy cannot be created or destroyed; it just gets converted between various forms. This means that the total amount of energy in any closed system does not change, but is constant (i.e., conserved). The word closed means that a system cannot exchange energy with other systems. For example, imagine a closed room whose walls are very thick and made of materials that allow no heat, light, radio, or any other form of energy to enter or exit. In this room, there are various stores of supplies, such as firewood, oil, and food, and there are appa-ratuses such as steam engines, water wheels, water pumps, and electrical generators. A person in this room could perform many tasks involving energy—move objects, boil water, drive steam-powered generators, power light bulbs, etc. But, all of these tasks involve only the conversion of energy from one form to another—not the creation or destruction of energy.
No longer available |Learn more- Irving Granet, Maurice Bluestein(Authors)
- 2014(Publication Date)
- CRC Press(Publisher)
In addition, it pos-sesses energy due to the internal attractive and repulsive forces between particles. These forces become the mechanism for energy storage whenever particles become separated, such as when a liquid evaporates or the body is subjected to a deformation by an external energy source. Also, energy may be stored in the rotation and vibration of the molecules. Additional amounts of energy are involved with the electron configuration within the atoms and with the nuclear particles. The energy from all such sources is called the inter-nal energy of the body and is designated by the symbol U . Per unit mass ( m ), the specific internal energy is denoted by the symbol u , where mu = U . Thus, mu U = (2.1) or u U m = (2.2) 64 Thermodynamics and Heat Power From a practical standpoint, the measurement of the absolute internal energy of a system in a given state presents an insurmountable problem and is not essential to our study of thermodynamics. We are concerned with changes in internal energy, and the arbitrary datum for the zero of internal energy will not enter into these problems. Just as it is possible to distinguish the various forms of energy, such as work and heat, in a mechanical system, it is equally possible to distinguish the various forms of energy associated with electrical, chemical, and other systems. For the purpose of this book, these forms of energy, work, and heat are not considered. Students are cautioned that if a system includes any forms of energy other than mechanical, these items must be included. For example, the energy that is dissipated in a resistor as heat when a current flows through it must be taken into account when all the energies of an electrical system are being considered. 2.5 Potential Energy Let us consider the following problem, illustrated in Figure 2.3, where a body of mass m is in a locality in which the local gravitational field is constant and equal to g .
eBook - PDF- Raymond Serway, Chris Vuille(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
The greater the original kinetic energy, the more the car is compressed during a collision, and the greater the damage. By using data obtained through crash tests, it’s possible to obtain effective spring constants for all the different models of cars and determine reliable estimates of the change in velocity of a given vehicle during an accident. Medical research has established the likelihood of spinal injury for a given change in velocity, and the estimated velocity change can be used to help reduce insurance fraud. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 5.6 | Systems and Energy Conservation 143 Recall, however, that the Total Mechanical Energy is given by E 5 KE 1 PE. Making this substitution into Equation 5.21, we find that the work done on a system by all nonconservative forces is equal to the change in mechanical energy of that system: W nc 5 E f 2 E i 5 DE [5.22] If the mechanical energy is changing, it has to be going somewhere. The energy either leaves the system and goes into the surrounding environment, or it stays in the system and is converted into a nonmechanical form such as thermal energy. A simple example is a block sliding along a rough surface. Friction creates thermal energy, absorbed partly by the block and partly by the surrounding envi- ronment. When the block warms up, something called internal energy increases. The internal energy of a system is related to its temperature, which in turn is a consequence of the activity of its parts, such as the motion of atoms in a gas or the vibration of atoms in a solid. (Internal energy will be studied in more detail in Topics 10 –12.) Energy can be transferred between a nonisolated system and its environment. If positive work is done on the system, energy is transferred from the environment to the system. If negative work is done on the system, energy is transferred from the system to the environment.
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